Question

Betsy is saying for a bird cage. She saves $1 the first week, $3 the second week, $9 the third week, and so on. All together how much money will she have saved in 5 weeks?

Answer 1

Answer:

Betsy will save $121 in 5 weeks.

Step-by-step explanation:

We can see that Betsy's savings are 3 times the saving of her last week. We can see that this is an geometric sequence as 1,3,9,..

To find the sum of our geometric sequence we will use $S_{n}=a\cdot \frac{1-r^{n}}{1-r}$, where n is number of terms we are taking sum of, a is first term of sequence and r is common ratio of the sequence.

$S_{5}=1\cdot \frac{1-3^{5}}{1-3}$

$S_{5}=\frac{1-243}{-2}$

$S_{n}=\frac{-242}{-2}=121$

Therefore, Betsy will save $121 in 5 weeks.